Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA PROELEM SOLVINGProblem solving prooesses throughproblem solving. (How else?) Developingone of the lists of problem-solvingapproaches (as to the right) through severalwell-chosen problems over a periodof time is one way to start.However,the prooesses must be emphasized andpraotioed frequently, just as computationalskills must be, if they are to becomematters of habit.Getting the studentsto try the approaches may require a"sell-job."Many middle schoolers wantto know specifically what-calculation-todorather than what-kind-of-thinking-todo.Unfortunately, problem-solving processeslike those in the list do notassure a solution.They do, however,give students some things to try when-­as is the case for "true" problems-­there is no obvious way to proceed.us briefly look at the steps listed tothe right.Understand the problem.LetAt minimumthis step includes knowing what is soughtand what information is given, and helpsto "get started" on the problem.Somestudents will have difficulty reading,...---------------,(STEPSIN PROBLEM SOLVING1. UNDERSTAND THE PROBLEM.2. DEVISE A PLAN.--DO YOU KNOW HOW TO SOLVEA SIMILAR PROBLEM?--SOLVE A SIMPLER PROBLEM--MAKE A DIAGRAM) TABLE)NUMBER LINE) GRAPH--SOLVE PART OF THE PROBLEM--GUESS AND CHECK--LOOK FOR PATTERNS--WRITE AN EQUATION3. CARRY OUT THE PLAN.4. LOOK BACK.--CHECK--WHAT METHOD(S) DID YOUUSE?--CAN YOU DO SIMILARPROBLEMS?--IS THERE ANOTHER SOLUTION?(Adapted from Polya, 1971.)word problems (see Reading in Mathematios in the resource Ratio, Proportion andscaltng); attention to vocabulary and emphasis on multiple, slow-paced readings mayhelp some students.Many teachers like to have their students paraphrase word problems.Paraphrasings at least assure that the students have read them and may helpsome break their "I can' tDevise a plan.understand word problems" block.Most often this step is the bottleneck, so more detail is givenin the list above. Let's look at Problem 5: What is the remainder when 5 999 isdivided by 71 (Some students will learn that the usual algorithm does not apply (directly to expressions like 5 999 .) "Do you know how to solve a similar problem?" \(24